Some remarks on large-time behaviors for the linearized compressible Navier-Stokes equations

In this paper, we consider the linearized compressible Navier-Stokes equations in the whole space Rⁿ. Concerning initial datum with suitable regularities, we introduce a new threshold |B₀|=0 to distinguish different large-time behaviors. Particularly in the lower-dimensions, optimal growth estimates ($n=1$ polynomial growth, $n=2$ logarithmic growth) hold when |B₀| > 0, whereas optimal decay estimates hold when |B₀|=0. Furthermore, we derive asymptotic profiles of solutions with weighted L¹ datum as large-time.